Mathlib Map

Theorems · Definition · number theory

NumberField.mixedEmbedding.realSpace

(K : Type u_1) → [Field K] → Type u_1

The realSpace associated to a number field K is the real vector space indexed by the infinite places of K.

Defined in
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic
Cited by
87 results in Mathlib
Foundations
Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Field

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

NumberField.mixedEmbedding.fundamentalCone.expMapBasis · cited by 30fundamentalCone.expMapBas…NumberField.mixedEmbedding.normAtAllPlaces · cited by 30mixedEmbedding.normAtAllP…NumberField.mixedEmbedding.fundamentalCone.expMap · cited by 23fundamentalCone.expMapNumberField.mixedEmbedding.mixedSpaceOfRealSpace · cited by 20mixedEmbedding.mixedSpace…NumberField.mixedEmbedding.fundamentalCone.paramSet · cited by 18fundamentalCone.paramSetNumberField.mixedEmbedding.fundamentalCone.completeBasis · cited by 16fundamentalCone.completeB…NumberField.mixedEmbedding.fundamentalCone.compactSet · cited by 11fundamentalCone.compactSetNumberField.mixedEmbedding.normAtComplexPlaces · cited by 8mixedEmbedding.normAtComp…NumberField.mixedEmbedding.fundamentalCone.expMapBasis_pos · cited by 7fundamentalCone.expMapBas…NumberField.mixedEmbedding.normAtPlace_mixedSpaceOfRealSpace · cited by 6mixedEmbedding.normAtPlac…NumberField.mixedEmbedding.fundamentalCone.completeFamily · cited by 5fundamentalCone.completeF…NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace · cited by 5fundamentalCone.realSpace…NumberField.mixedEmbedding.fundamentalCone.normLeOne_eq_preimage · cited by 4fundamentalCone.normLeOne…NumberField.mixedEmbedding.fundamentalCone.closure_paramSet · cited by 3fundamentalCone.closure_p…NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne · cited by 3fundamentalCone.completeB…Real · cited by 25697RealField · cited by 7404FieldNumberField.InfinitePlace · cited by 604NumberField.InfinitePlacemixedEmbedding.realSpaceCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by99

Results whose statement or proof uses this declaration.